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Benedict Irwin edited Slater Determinants.tex
over 9 years ago
Commit id: b26442f49f8a9aa0404e986a207cfa6a9dc6cbd2
deletions | additions
diff --git a/Slater Determinants.tex b/Slater Determinants.tex
index 7069057..2f53005 100644
--- a/Slater Determinants.tex
+++ b/Slater Determinants.tex
...
\sqrt{2}\Psi(r_1,r_2)=\phi_1(r_1)\phi_2(r_2)-\phi_2(r_1)\phi_1(r_2) = \Psi(r_1)\phi_2(r_2)-\phi_2(r_1)\Psi(r_2) \\
\sqrt{6}\Psi(r_1,r_2,r_3)=\dots=\Psi(r_1,r_2)\phi_3(r_3)+\Psi(r_2,r_3)\phi_3(r_1)+\Psi(r_3,r_1)\phi_3(r_2)
\end{equation}
This ends with \begin{equation}
\Psi(r_1\dots r_N)=\frac{1}{\sqrt{N!}}\sum_{i=1}^n \Psi(r_{i+1 mod N?},r_{i+2 mod N?}\dots r_{N mod N?})\phi_N(r_i)
\end{equation}